A system composed of n separate components is said to be a p

A system composed of n separate components is said to be a parallel system if it functions when at least one of the components functions. Suppose the following systems function if current flows from A to B. If each switch (break in the line) is activated (i.e. closed to allow electricity to flow across the line) independently with probability p = 0.3, what is the probability the system functions? Solve for each circuit.

Solution

Using the complement rule, the probability that the system functions is

1 - P(doesn’tfunction).

So, P(functions) = 1-0.7^4= 0.7599